Let G=(V, E) be a simple graph with n vertices, m edges and p connected components. The problem of constructing a spanning forest is to find a spanning tree for each connected component of G. For a simple graph, Chin et al.[4] demonstrated that a spanning forest can be found in O(log^2 n) time using O(n^2/log^2 n) processors. In this paper, we propose an O(log n) time parallel algorithm with O(n/log n) processors on the EREW PRAM for constructing a spanning forest on Interval graphs.